Wednesday, September 24, 2025

The Hilbert mapping

In the 1980s, computers got good enough to display fractal patterns to the home audience. James Gleick put out Chaos at about the right time, for the PC-Jr. In mid 1990 I figured out how to render some of these for the school Nimbus (remember that?). We're here to talk the Hilbert tasselation.

Hilbert rendered your 1D array into a 2D spacefilling curve. It is, or maybe was, considered superior to the usual x + y*maxx mapping since proximity in the array would approximate proximity in the mapped plane, also. Hilbert himself used the square grid; Gosper's flowsnake does it for the hexagonal beehive.

In 1984 Antonin Guttman invented the R-tree, which indexes multidimensional objects: "find bookstores within two miles". Hilbert gained a real lease on life here. To be noted, I think technically Gosper is better out of doors, as a wilderness map.

Hilbert's classic square, rather, has use in human-visualising the nature of 1D data. It also compresses images and/or dithers them.

BACKDATE 9.26

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